Single-flux-quantum (SFQ) logic is promising technology to realize an incredible microprocessor which operates over 100 GHz due to its ultra-fast-speed and ultra-low-power natures. Although previous work has demonstrated prototype of an SFQ microprocessor, the SFQ based L1 cache memory has not well optimized: a large access latency and strictly limited scalability. This paper proposes a novel SFQ cache architecture to support fast accesses. The sub-arrayed structure applied to the cache produces better scalability in terms of capacity. Evaluation results show that the proposed cache achieves 1.8X fast access speed.